Senate leaders showed bipartisan support Sunday for tougher sanctions on Iran following failed talks this weekend toward curtailing that country’s nuclear-development program, but also indicated they would likely wait until after talking to Secretary of State John Kerry.

Kerry and other Western leaders wrapped up talks Sunday after failing to agree on a deal, which purportedly stalled when France rejected a list of demands on Iran because they were too generous to mean an easing of international sanctions.

Administration officials led by Vice President Joe Biden and including Kerry had persuaded senators late last month to delay considering a new round of penalties until after the Geneva talks.

Sen. Bob Menendez, chairman of the Senate Foreign Relations Committee, said those talks are done and suggested new sanctions would serve as an insurance policy for those wary about the new Iranian government’s promises.

"It's an insurance for the United States to make sure that Iran actually complies with an agreement that we would want to see," he told ABC’s “This Week.”

He said they would also send to Iran the message: “You know what’s coming.”

Much of the world believes Iran is pursing the development of a nuclear weapon and has imposed crippling economic sanctions, though the Middle East country has denied the accusation.

South Carolina GOP Sen. Lindsey Graham said sanctions have brought Iran to the negotiating table and "if we back off now, I think that's exactly the wrong signal."

He told CNN's "State of the Union" that "a new round of sanctions will be coming from the Congress. The Congress will define the end game because we're worried about the end game, not some interim deal. You can't trust the Iranians."

In the broader region, he said, "the Israelis are apoplectic about what we're doing. I've never been more worried about the Obama administration's approach to the Mideast then I am now."

However, Tennessee Republican Sen. Bob Corker, a member of the Senate Foreign Relations Committee, said the chamber’s Democratic leadership had called off a Senate Banking, Housing and Urban Affairs Committee session this week to examine proposed sanctions and that Kerry would be on Capitol Hill to brief lawmakers about Iran.

"I do know that on both sides of the Capitol, on both sides of the aisle right now, people are really looking at what the next steps ought to be," Corker told NBC’s “Meet the Press.”

"All of us want to see diplomacy,” he continued. “That is the best way to resolve this issue. But we're also concerned about an administration that seems really ready always to jump into the arms of folks and potentially deal away some of the leverage we have."

Corker said new penalties would not kick in for several months, and that the current sanctions could be toned down, if necessary, based on Iran's actions.

"I think this week sitting down, talking with Secretary Kerry is going to be an important element of what we do,” he added. “We know the sanctions have gotten us here, and we're worried we're dealing away with our leverage."

The Associated Press contributed to this report.